Vasicek Model for Interest Rate Modelling

The Vasicek model assumes a mean-reverting process for short-term interest rates. The basic assumption is that the economy has an equilibrium level based on economic fundamentals such as long-run monetary supply, technological innovations, and similar factors. Therefore, if the short-term rate is above the long-run equilibrium value, the drift adjustment will be negative to bring the current rate closer to its mean-reverting level.

dr = k(θ − r)dt + σdw

where:
k = a parameter that measures the speed of reversion adjustment
θ = long-run value of the short-term rate assuming risk neutrality
r = current interest rate level

Why is Vasicek Model important?

The mean reversion parameter used in the model helps in improving the specification of the term structure. Further, it also produces a specific term structure of declining volatility. Therefore, short-term volatility is over-stated, and long-term volatility is understated.